scipy.fftpack.idct¶

scipy.fftpack.idct(x, type=2, n=None, axis=- 1, norm=None, overwrite_x=False)[source]

Return the Inverse Discrete Cosine Transform of an arbitrary type sequence.

Parameters
xarray_like

The input array.

type{1, 2, 3, 4}, optional

Type of the DCT (see Notes). Default type is 2.

nint, optional

Length of the transform. If `n < x.shape[axis]`, x is truncated. If `n > x.shape[axis]`, x is zero-padded. The default results in `n = x.shape[axis]`.

axisint, optional

Axis along which the idct is computed; the default is over the last axis (i.e., `axis=-1`).

norm{None, ‘ortho’}, optional

Normalization mode (see Notes). Default is None.

overwrite_xbool, optional

If True, the contents of x can be destroyed; the default is False.

Returns
idctndarray of real

The transformed input array.

`dct`

Forward DCT

Notes

For a single dimension array x, `idct(x, norm='ortho')` is equal to MATLAB `idct(x)`.

‘The’ IDCT is the IDCT of type 2, which is the same as DCT of type 3.

IDCT of type 1 is the DCT of type 1, IDCT of type 2 is the DCT of type 3, and IDCT of type 3 is the DCT of type 2. IDCT of type 4 is the DCT of type 4. For the definition of these types, see `dct`.

Examples

The Type 1 DCT is equivalent to the DFT for real, even-symmetrical inputs. The output is also real and even-symmetrical. Half of the IFFT input is used to generate half of the IFFT output:

```>>> from scipy.fftpack import ifft, idct
>>> ifft(np.array([ 30.,  -8.,   6.,  -2.,   6.,  -8.])).real
array([  4.,   3.,   5.,  10.,   5.,   3.])
>>> idct(np.array([ 30.,  -8.,   6.,  -2.]), 1) / 6
array([  4.,   3.,   5.,  10.])
```